# Machine-Learning Approaches for the Discovery of Electrolyte Materials for Solid-State Lithium Batteries

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

_{2}S-P

_{2}S

_{5}, which showed no sign of degradation up to 100 cycles at a high operating temperature of 170 °C and low temperature down to −40 °C [7,8]. The known good solid-state lithium-ion conductors could be characterised into different types depending on their compositions. For example, lithium thiophosphates (e.g., Li

_{10}GeP

_{2}S

_{12}), garnet (e.g., Li

_{7}Li

_{3}Zr

_{2}O

_{12}), NASICON (e.g., Li

_{1.3}Al

_{0.3}Ti

_{1.7}(PO

_{4})

_{3}), perovskite (e.g., Li

_{0.5}La

_{0.5}TiO

_{3}), and argyrodite (e.g., Li

_{6}PS

_{5}Cl) [9,10,11,12,13]. These conductors exhibit fast lithium-ion conduction properties, with relatively high ionic conductivities at room temperature (RT) compared with other lithium conductors. However, they are still far from large-scale production and application due to lacking well-rounded properties [14]. The early discovered lithium nitride (Li

_{3}N) has a high ionic conductivity of 6 × 10

^{−3}S cm

^{−1}at RT, but it shows low electrochemical stabilities [15]. On the other hand, polymer electrolytes, such as polyethylene oxide, generally have significantly lower conductivities than common liquid electrolytes, which are unattractive for commercialisation [16,17]. Therefore, further research in discovering new solid-state lithium-ion conductors are needed.

## 2. Discovery and Screening Methods of New Materials for SSEs

## 3. Typical Machine Learning Techniques Used in Materials Discovery

#### 3.1. Supervised Learning

#### 3.2. Unsupervised Learning

## 4. Machine Learning Applications for Materials Discovery of SSEs

_{4}GeO

_{4}had the highest predictive conductivity at 373 K, which was reported as approximately 5.5 × 10

^{−4}S cm

^{−1}from the ML model. It could potentially exceed the conductivity of LISICON (Li

_{3.5}Zn

_{0.25}GeO

_{4}) by a significant amount. However, primarily due to the difficulties in synthesising γ-Li

_{4}GeO

_{4}, further experiments are expected for the prediction validations to evaluate this candidate as one of the next-generation SSE materials. Guo et al. mapped the lithium thiophosphate (LPS) phase diagram by combining first-principles and artificial intelligence (AI) methods, integrating DFT, artificial neural network potentials, genetic algorithm sampling, and ab initio molecular dynamics simulations [84]. Based on the discovered trends in the LPS phase diagram, Guo et al. propose a candidate solid-state electrolyte composition, (Li

_{2}S)

_{x}(P

_{2}S

_{5})

_{1−x}(x~0.725), that exhibits high ionic conductivity of >10

^{−2}S cm

^{−1}, demonstrating a design strategy for amorphous or glassy/ceramic solid electrolytes [84].

_{8}N

_{2}Se, Li

_{6}KBiO

_{6}and Li

_{5}P

_{2}N

_{5}, had conductivities exceeding the best-known lithium fast-conductors, which showed the effectiveness of the clustering techniques. However, some materials did not exhibit high conductivity values in the simulation, and the clustering results might be improved by further research in the featurisation of the clustering input. In addition, experimental validations are required to investigate the fast-conducting SSE candidates from the AIMD simulation.

^{−1}boundary of ionic conductivity. The model predicted 317 fast-ion lithium-conducting materials from over 12,000 inputs, and 21 crystalline compounds were identified as promising candidates with desired structural and electrochemical stability. Only one false positive material prediction was reported as LiCl obtains poor conduction properties from the literature. DFT-MD was then performed for identified candidates with unknown conductivity at 900 K to evaluate the performance of the ML model. With scaling to RT based on the Arrhenius relationship, eight candidates exhibit high ionic conductivity at RT. In particular, Li

_{5}B

_{7}S

_{13}exhibited a conductivity of 74 mS cm

^{−1}, which is many times higher than the best-known lithium conductors. In addition, the ML-based approach showed a much higher efficiency and accuracy for predicting superionic materials compared with a random selection from 317 materials and Ph.D. student screening [87]. With further experimental research, these eight candidates could be promising materials for SSEs.

_{3}and Li

_{2}MgO

_{2}. While some compounds were studied before, further investigations are required for other candidate materials. Table 1 summarises the algorithms and approaches used in the literature and compares their advantages and disadvantages.

## 5. Conclusions and Future Directions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

SSE | Solid-State Electrolyte |

ML | Machine Learning |

DFT | Density Functional Theory |

AIMD | Ab Initio Molecular Dynamics |

kMC | Kinetic Monte Carlo |

SVM | Support Vector Machine |

SVR | Support Vector Regression |

ICSD | Inorganic Crystal Structure Database |

mXRD | Modified X-ray Diffraction |

DFT-MD | Density Functional Theory Molecular Dynamics |

RT | Room Temperature |

## References

- Assad, M.; Rosen, M.A.A. (Eds.) Design and Performance Optimization of Renewable Energy Systems; Elsevier: Amsterdam, The Netherlands, 2021. [Google Scholar] [CrossRef]
- Yang, Z.; Huang, H.; Lin, F.; Yang, Z.; Lin, F.; Huang, H. Sustainable Electric Vehicle Batteries for a Sustainable World: Perspectives on Battery Cathodes, Environment, Supply Chain, Manufacturing, Life Cycle, and Policy. Adv. Energy Mater.
**2022**, 12, 2200383. [Google Scholar] [CrossRef] - Wen, J.; Yu, Y.; Chen, C. A Review on Lithium-Ion Batteries Safety Issues: Existing Problems and Possible Solutions. Mater. Express
**2012**, 2, 197–212. [Google Scholar] [CrossRef] - Pigłowska, M.; Kurc, B.; Galiński, M.; Fuć, P.; Kamińska, M.; Szymlet, N.; Daszkiewicz, P. Challenges for Safe Electrolytes Applied in Lithium-Ion Cells—A Review. Materials
**2021**, 14, 6783. [Google Scholar] [CrossRef] [PubMed] - Lin, D.; Liu, Y.; Cui, Y. Reviving the Lithium Metal Anode for High-Energy Batteries. Nat. Nanotechnol.
**2017**, 12, 194–206. [Google Scholar] [CrossRef] - Xu, L.; Tang, S.; Cheng, Y.; Wang, K.; Liang, J.; Liu, C.; Cao, Y.C.; Wei, F.; Mai, L. Interfaces in Solid-State Lithium Batteries. Joule
**2018**, 2, 1991–2015. [Google Scholar] [CrossRef] - Ogawa, M.; Yoshida, K.; Harada, K. All-Solid-State Lithium Batteries with Wide Operating Temperature Range. SEI Tech. Rev.
**2012**, 74, 88–90. [Google Scholar] - Zheng, F.; Kotobuki, M.; Song, S.; Lai, M.O.; Lu, L. Review on Solid Electrolytes for All-Solid-State Lithium-Ion Batteries. J. Power Sources
**2018**, 389, 198–213. [Google Scholar] [CrossRef] - Kamaya, N.; Homma, K.; Yamakawa, Y.; Hirayama, M.; Kanno, R.; Yonemura, M.; Kamiyama, T.; Kato, Y.; Hama, S.; Kawamoto, K.; et al. A Lithium Superionic Conductor. Nat. Mater.
**2011**, 10, 682–686. [Google Scholar] [CrossRef] - Kumazaki, S.; Iriyama, Y.; Kim, K.H.; Murugan, R.; Tanabe, K.; Yamamoto, K.; Hirayama, T.; Ogumi, Z. High Lithium Ion Conductive Li
_{7}La_{3}Zr_{2}O_{12}by Inclusion of Both Al and Si. Electrochem. Commun.**2011**, 13, 509–512. [Google Scholar] [CrossRef] - Aono, H.; Sugimoto, E.; Sadaoka, Y.; Imanaka, N.; Adachi, G. Ionic Conductivity and Sinterability of Lithium Titanium Phosphate System. Solid State Ion.
**1990**, 40–41, 38–42. [Google Scholar] [CrossRef] - Ibarra, J.; Várez, A.; León, C.; Santamaría, J.; Torres-Martínez, L.M.; Sanz, J. Influence of Composition on the Structure and Conductivity of the Fast Ionic Conductors La
_{2/3}−_{x}Li_{3x}TiO_{3}(0.03 ≤ x ≤ 0.167). Solid State Ion.**2000**, 134, 219–228. [Google Scholar] [CrossRef] - Boulineau, S.; Courty, M.; Tarascon, J.M.; Viallet, V. Mechanochemical Synthesis of Li-Argyrodite Li6PS5X (X = Cl, Br, I) as Sulfur-Based Solid Electrolytes for All Solid State Batteries Application. Solid State Ion.
**2012**, 221, 1–5. [Google Scholar] [CrossRef] - Zhu, Y.; He, X.; Mo, Y. Origin of Outstanding Stability in the Lithium Solid Electrolyte Materials: Insights from Thermodynamic Analyses Based on First-Principles Calculations. ACS Appl. Mater. Interfaces
**2015**, 7, 23685–23693. [Google Scholar] [CrossRef] - Lapp, T.; Skaarup, S.; Hooper, A. Ionic Conductivity of Pure and Doped Li3N. Solid State Ion.
**1983**, 11, 97–103. [Google Scholar] [CrossRef] - Edman, L.; Ferry, A.; Doeff, M.M. Slow Recrystallization in the Polymer Electrolyte System Poly(Ethylene Oxide)
_{n}-LiN(CF^{3}SO^{2})_{2}. J. Mater. Res.**2000**, 15, 1950–1954. [Google Scholar] [CrossRef] - Croce, F.; Appetecchi, G.B.; Persi, L.; Scrosati, B. Nanocomposite Polymer Electrolytes for Lithium Batteries. Nature
**1998**, 394, 456–458. [Google Scholar] [CrossRef] - Porz, L.; Swamy, T.; Sheldon, B.W.; Rettenwander, D.; Frömling, T.; Thaman, H.L.; Berendts, S.; Uecker, R.; Carter, W.C.; Chiang, Y.M. Mechanism of Lithium Metal Penetration through Inorganic Solid Electrolytes. Adv. Energy Mater.
**2017**, 7, 1701003. [Google Scholar] [CrossRef] - Bai, P.; Li, J.; Brushett, F.R.; Bazant, M.Z. Transition of Lithium Growth Mechanisms in Liquid Electrolytes. Energy Environ. Sci.
**2016**, 9, 3221–3229. [Google Scholar] [CrossRef] - Koerver, R.; Zhang, W.; de Biasi, L.; Schweidler, S.; Kondrakov, A.O.; Kolling, S.; Brezesinski, T.; Hartmann, P.; Zeier, W.G.; Janek, J. Chemo-Mechanical Expansion of Lithium Electrode Materials—On the Route to Mechanically Optimized All-Solid-State Batteries. Energy Environ. Sci.
**2018**, 11, 2142–2158. [Google Scholar] [CrossRef] - Koerver, R.; Aygün, I.; Leichtweiß, T.; Dietrich, C.; Zhang, W.; Binder, J.O.; Hartmann, P.; Zeier, W.G.; Janek, J. Capacity Fade in Solid-State Batteries: Interphase Formation and Chemomechanical Processes in Nickel-Rich Layered Oxide Cathodes and Lithium Thiophosphate Solid Electrolytes. Chem. Mater.
**2017**, 29, 5574–5582. [Google Scholar] [CrossRef] - Bucci, G.; Talamini, B.; Renuka Balakrishna, A.; Chiang, Y.M.; Carter, W.C. Mechanical Instability of Electrode-Electrolyte Interfaces in Solid-State Batteries. Phys. Rev. Mater.
**2018**, 2, 105407. [Google Scholar] [CrossRef] - De Pablo, J.J.; Jackson, N.E.; Webb, M.A.; Chen, L.-Q.; Moore, J.E.; Morgan, D.; Jacobs, R.; Pollock, T.; Schlom, D.G.; Toberer, E.S. New Frontiers for the Materials Genome Initiative. Npj Comput. Mater.
**2019**, 5, 41. [Google Scholar] [CrossRef] - Yang, K.; Setyawan, W.; Wang, S.; Buongiorno Nardelli, M.; Curtarolo, S. A Search Model for Topological Insulators with High-Throughput Robustness Descriptors. Nat. Mater.
**2012**, 11, 614–619. [Google Scholar] [CrossRef] [PubMed] - Wang, S.; Wang, Z.; Setyawan, W.; Mingo, N.; Curtarolo, S. Assessing the Thermoelectric Properties of Sintered Compounds via High-Throughput Ab-Initio Calculations. Phys. Rev.
**2011**, 1, 021012. [Google Scholar] [CrossRef] - Curtarolo, S.; Hart, G.L.W.; Nardelli, M.B.; Mingo, N.; Sanvito, S.; Levy, O. The High-Throughput Highway to Computational Materials Design. Nat. Mater.
**2013**, 12, 191–201. [Google Scholar] [CrossRef] - Yu, L.; Zunger, A. Identification of Potential Photovoltaic Absorbers Based on First-Principles Spectroscopic Screening of Materials. Phys. Rev. Lett.
**2012**, 108, 068701. [Google Scholar] [CrossRef] - Greeley, J.; Jaramillo, T.F.; Bonde, J.; Chorkendorff, I.; Nørskov, J.K. Computational High-Throughput Screening of Electrocatalytic Materials for Hydrogen Evolution. Nat. Mater.
**2006**, 5, 909–913. [Google Scholar] [CrossRef] - Nørskov, J.K.; Bligaard, T.; Rossmeisl, J.; Christensen, C.H. Towards the Computational Design of Solid Catalysts. Nat. Chem.
**2009**, 1, 37–46. [Google Scholar] [CrossRef] - Jain, A.; Shin, Y.; Persson, K.A. Computational Predictions of Energy Materials Using Density Functional Theory. Nat. Rev. Mater.
**2016**, 1, 15004. [Google Scholar] [CrossRef] - Frenkel, D.; Smit, B. Understanding Molecular Simulation: From Algorithms to Applications; Elsveier: Amsterdam, The Netherlands, 2001; ISBN 9780080519982. [Google Scholar]
- Marx, D.; Hutter, J. Ab Initio Molecular Dynamics: Basic Theory and Advanced Methods; Cambridge University Press: Cambridge, UK, 2009; ISBN 9780521898638. [Google Scholar]
- van der Ven, A.; Ceder, G.; Asta, M.; Tepesch, P.D. First-Principles Theory of Ionic Diffusion with Nondilute Carriers. Phys. Rev. B
**2001**, 64, 184307. [Google Scholar] [CrossRef] - van der Ven, A.; Thomas, J.C.; Xu, Q.; Swoboda, B.; Morgan, D. Nondilute Diffusion from First Principles: Li Diffusion in Lix TiS2. Phys. Rev. B-Condens. Matter Mater. Phys.
**2008**, 78, 104306. [Google Scholar] [CrossRef] - Bulnes, F.M.; Pereyra, V.D.; Riccardo, J.L. Collective Surface Diffusion: N-Fold Way Kinetic Monte Carlo Simulation. Phys. Rev E
**1998**, 58, 86. [Google Scholar] [CrossRef] - Voter, A.F. Introduction to the Kinetic Monte Carlo Method. Radiat. Eff. Solids
**2007**, 235, 1–23. [Google Scholar] [CrossRef] - Chen, W.; Li, Y.; Feng, D.; Lv, C.; Li, H.; Zhou, S.; Jiang, Q.; Yang, J.; Gao, Z.; He, Y.; et al. Recent Progress of Theoretical Research on Inorganic Solid State Electrolytes for Li Metal Batteries. J. Power Sources
**2023**, 561, 232720. [Google Scholar] [CrossRef] - Baktash, A.; Reid, J.C.; Yuan, Q.; Roman, T.; Searles, D.J.; Baktash, A.; Reid, J.C.; Yuan, Q.; Roman, T.; Searles, D.J. Shaping the Future of Solid-State Electrolytes through Computational Modeling. Adv. Mater.
**2020**, 32, 1908041. [Google Scholar] [CrossRef] - Hao, F.; Mukherjee, P.P. Mesoscale Analysis of the Electrolyte-Electrode Interface in All-Solid-State Li-Ion Batteries. J. Electrochem. Soc.
**2018**, 165, A1857–A1864. [Google Scholar] [CrossRef] - Bo, Z.; Li, H.; Yang, H.; Li, C.; Wu, S.; Xu, C.; Xiong, G.; Mariotti, D.; Yan, J.; Cen, K.; et al. Combinatorial Atomistic-to-AI Prediction and Experimental Validation of Heating Effects in 350 F Supercapacitor Modules. Int. J. Heat Mass Transf.
**2021**, 171, 121075. [Google Scholar] [CrossRef] - Jalem, R.; Aoyama, T.; Nakayama, M.; Nogami, M. Multivariate Method-Assisted Ab Initio Study of Olivine-Type LiMXO
_{4}(Main Group M^{2+}-X^{5+}and M^{3+}-X^{4+}) Compositions as Potential Solid Electrolytes. Chem. Mater.**2012**, 24, 1357–1364. [Google Scholar] [CrossRef] - Pirouz, D.M.; Student, D. An Overview of Partial Least Squares; University of California: Los Angeles, CA, USA, 2006. [Google Scholar]
- Sendek, A.D.; Yang, Q.; Cubuk, E.D.; Duerloo, K.A.N.; Cui, Y.; Reed, E.J. Holistic Computational Structure Screening of More than 12000 Candidates for Solid Lithium-Ion Conductor Materials. Energy Environ. Sci.
**2017**, 10, 306–320. [Google Scholar] [CrossRef] - Sendek, A.D.; Ransom, B.; Cubuk, E.D.; Pellouchoud, L.A.; Nanda, J.; Reed, E.J. Machine Learning Modeling for Accelerated Battery Materials Design in the Small Data Regime. Adv. Energy Mater.
**2022**, 12, 2200553. [Google Scholar] [CrossRef] - Regonia, P.R.; Pelicano, C.M.; Tani, R.; Ishizumi, A.; Yanagi, H.; Ikeda, K. Predicting the Band Gap of ZnO Quantum Dots via Supervised Machine Learning Models. Optik
**2020**, 207, 164469. [Google Scholar] [CrossRef] - Pei, J.-F.; Cai, C.-Z.; Zhu, Y.-M.; Yan, B. Modeling and Predicting the Glass Transition Temperature of Polymethacrylates Based on Quantum Chemical Descriptors by Using Hybrid PSO-SVR. Macromol. Theory Simul.
**2013**, 22, 52–60. [Google Scholar] [CrossRef] - Fang, S.F.; Wang, M.P.; Qi, W.H.; Zheng, F. Hybrid Genetic Algorithms and Support Vector Regression in Forecasting Atmospheric Corrosion of Metallic Materials. Comput. Mater. Sci.
**2008**, 44, 647–655. [Google Scholar] [CrossRef] - Balachandran, P.V.; Theiler, J.; Rondinelli, J.M.; Lookman, T. Materials Prediction via Classification Learning. Sci. Rep.
**2015**, 5, 13285. [Google Scholar] [CrossRef] [PubMed] - Isayev, O.; Fourches, D.; Muratov, E.N.; Oses, C.; Rasch, K.; Tropsha, A.; Curtarolo, S. Materials Cartography: Representing and Mining Materials Space Using Structural and Electronic Fingerprints. Chem. Mater.
**2015**, 27, 735–743. [Google Scholar] [CrossRef] - Zhou, Q.; Tang, P.; Liu, S.; Pan, J.; Yan, Q.; Zhang, S.C. Learning Atoms for Materials Discovery. Proc. Natl. Acad. Sci. USA
**2018**, 115, E6411–E6417. [Google Scholar] [CrossRef] - Long, C.J.; Hattrick-Simpers, J.; Murakami, M.; Srivastava, R.C.; Takeuchi, I.; Karen, V.L.; Li, X. Rapid Structural Mapping of Ternary Metallic Alloy Systems Using the Combinatorial Approach and Cluster Analysis. Rev. Sci. Instrum.
**2007**, 78, 072217. [Google Scholar] [CrossRef] - Kireeva, N.; Baskin, I.I.; Gaspar, H.A.; Horvath, D.; Marcou, G.; Varnek, A. Generative Topographic Mapping (GTM): Universal Tool for Data Visualization, Structure-Activity Modeling and Dataset Comparison. Mol. Inform.
**2012**, 31, 301–312. [Google Scholar] [CrossRef] - Zhang, Y.; He, X.; Chen, Z.; Bai, Q.; Nolan, A.M.; Roberts, C.A.; Banerjee, D.; Matsunaga, T.; Mo, Y.; Ling, C. Unsupervised Discovery of Solid-State Lithium Ion Conductors. Nat. Commun.
**2019**, 10, 5260. [Google Scholar] [CrossRef] - Alharin, A.; Doan, T.N.; Sartipi, M. Reinforcement Learning Interpretation Methods: A Survey. IEEE Access
**2020**, 8, 171058–171077. [Google Scholar] [CrossRef] - Zhou, Z.-H. Machine Learning; Springer Singapore: Singapore, 2021; ISBN 978-981-15-1966-6. [Google Scholar]
- Bell, J. Machine Learning; John Wiley & Sons, Inc.: Indianapolis, IN, USA, 2014; ISBN 9781119183464. [Google Scholar]
- Matloff, N. From Linear Models to Machine Learning Regression and Classification, with R Examples; University of California: Los Angeles, CA, USA, 2017. [Google Scholar]
- Utkin, L. An Imprecise Extension of SVM-Based Machine Learning Models. Neurocomputing
**2019**, 331, 18–32. [Google Scholar] [CrossRef] - Battineni, G.; Chintalapudi, N.; Amenta, F. Machine Learning in Medicine: Performance Calculation of Dementia Prediction by Support Vector Machines (SVM). Inform. Med. Unlocked
**2019**, 16, 100200. [Google Scholar] [CrossRef] - Vapnik, V.N. The Nature of Statistical Learning Theory; Springer: Berlin/Heidelberg, Germany, 2000. [Google Scholar] [CrossRef]
- Noble, W.S. What Is a Support Vector Machine? Nat. Biotechnol.
**2006**, 24, 1565–1567. [Google Scholar] [CrossRef] - Gavriilidis, A.; Velten, J.; Tilgner, S.; Kummert, A. Machine Learning for People Detection in Guidance Functionality of Enabling Health Applications by Means of Cascaded SVM Classifiers. J. Frankl. Inst.
**2018**, 355, 2009–2021. [Google Scholar] [CrossRef] - Kotenko, I.; Saenko, I.; Branitskiy, A. Improving the Performance of Manufacturing Technologies for Advanced Material Processing Using a Big Data and Machine Learning Framework. Mater. Today Proc.
**2019**, 11, 380–385. [Google Scholar] [CrossRef] - Zhao, H.; Ezeh, C.I.; Ren, W.; Li, W.; Pang, C.H.; Zheng, C.; Gao, X.; Wu, T. Integration of Machine Learning Approaches for Accelerated Discovery of Transition-Metal Dichalcogenides as Hg0 Sensing Materials. Appl. Energy
**2019**, 254, 113651. [Google Scholar] [CrossRef] - Chen, W.; Pourghasemi, H.R.; Kornejady, A.; Zhang, N. Landslide Spatial Modeling: Introducing New Ensembles of ANN, MaxEnt, and SVM Machine Learning Techniques. Geoderma
**2017**, 305, 314–327. [Google Scholar] [CrossRef] - Chang, C.-C.; Lin, C.-J. LIBSVM: A Library for Support Vector Machines. ACM Trans. Intell. Syst. Technol. (TIST)
**2001**, 2, 1–27. [Google Scholar] [CrossRef] - Anusha, K.S.; Ramanathan, R.; Jayakumar, M. Link Distance-Support Vector Regression (LD-SVR) Based Device Free Localization Technique in Indoor Environment. Eng. Sci. Technol. Int. J.
**2020**, 23, 483–493. [Google Scholar] [CrossRef] - Yu, C.; Fan, W.; Yu, H.; Si, F. A Machine Learning NOxemission Model for SCR System Considering Mechanism Knowledge and Catalyst Deactivation. E3S Web Conf.
**2020**, 194, 04064. [Google Scholar] [CrossRef] - Jain, A.K.; Dubes, R.C. Algorithms for Clustering Data; Prentice Hall: Hoboken, NJ, USA, 1988; ISBN 978-0-13-022278-7. [Google Scholar]
- Kaufman, L.; Rousseeuw, P.J. Finding Groups in Data: An Introduction to Cluster Analysis; Kaufman, L., Rousseeuw, P.J., Eds.; Wiley Series in Probability and Statistics; John Wiley & Sons, Inc.: Hoboken, NJ, USA, 1990; ISBN 9780470316801. [Google Scholar]
- Jain, A.K. Data Clustering: 50 Years Beyond K-Means. Mach. Learn. Knowl. Discov. Databases
**2008**, 1 Pt 19, 3–4. [Google Scholar] [CrossRef] - Alhawarat, M.; Hegazi, M. Revisiting K-Means and Topic Modeling, a Comparison Study to Cluster Arabic Documents. IEEE Access
**2018**, 6, 42740–42749. [Google Scholar] [CrossRef] - von Luxburg, U. A Tutorial on Spectral Clustering. Stat. Comput.
**2007**, 17, 395–416. [Google Scholar] [CrossRef] - Zhao, J.; Li, X.; Yu, D.; Zhang, J.; Zhang, W. Lithium-Ion Battery State of Health Estimation Using Meta-heuristic Optimization and Gaussian Process Regression. J. Energy Storag.
**2023**, 58, 106319. [Google Scholar] [CrossRef] - Zhuzhunashvili, D.; Knyazev, A. Preconditioned Spectral Clustering for Stochastic Block Partition Streaming Graph Challenge. In Proceedings of the 2017 IEEE High Performance Extreme Computing Conference, Waltham, MA, USA, 12–14 September 2017. [Google Scholar] [CrossRef]
- Bolla, M. Spectral Clustering and Biclustering: Learning Large Graphs and Contingency Tables; John Wiley & Sons, Ltd.: Hoboken, NJ, USA, 2013; pp. 1–268. [Google Scholar] [CrossRef]
- Sinaga, K.P.; Yang, M.S. Unsupervised K-Means Clustering Algorithm. IEEE Access
**2020**, 8, 80716–80727. [Google Scholar] [CrossRef] - Likas, A.; Vlassis, N.J.; Verbeek, J. The Global K-Means Clustering Algorithm. Pattern Recognit.
**2003**, 36, 451–461. [Google Scholar] [CrossRef] - Murtagh, F.; Contreras, P. Algorithms for Hierarchical Clustering: An Overview. Wiley Interdiscip. Rev. Data Min. Knowl. Discov.
**2012**, 2, 86–97. [Google Scholar] [CrossRef] - Espinoza, F.A.; Oliver, J.M.; Wilson, B.S.; Steinberg, S.L. Using Hierarchical Clustering and Dendrograms to Quantify the Clustering of Membrane Proteins. Bull. Math. Biol.
**2012**, 74, 190. [Google Scholar] [CrossRef] - Sasirekha, K.; Baby, P. Agglomerative Hierarchical Clustering Algorithm-A Review. Int. J. Sci. Res. Publ.
**2013**, 83, 83. [Google Scholar] - Murtagh, F.; Legendre, P. Ward’s Hierarchical Agglomerative Clustering Method: Which Algorithms Implement Ward’s Criterion? J. Classif.
**2014**, 31, 274–295. [Google Scholar] [CrossRef] - Fujimura, K.; Seko, A.; Koyama, Y.; Kuwabara, A.; Kishida, I.; Shitara, K.; Fisher, C.A.J.; Moriwake, H.; Tanaka, I. Accelerated Materials Design of Lithium Superionic Conductors Based on First-Principles Calculations and Machine Learning Algorithms. Adv. Energy Mater.
**2013**, 3, 980–985. [Google Scholar] [CrossRef] - Guo, H.; Wang, Q.; Urban, A.; Artrith, N. Artificial Intelligence-Aided Mapping of the Structure-Composition-Conductivity Relationships of Glass-Ceramic Lithium Thiophosphate Electrolytes. Chem. Mater.
**2022**, 34, 6702–6712. [Google Scholar] [CrossRef] - Bergerhoff, G.; Hundt, R.; Sievers, R.; Brown, I.D. The Inorganic Crystal Structure Data Base. J. Chem. Inf. Model.
**1983**, 23, 66–69. [Google Scholar] [CrossRef] - Jain, A.; Ong, S.P.; Hautier, G.; Chen, W.; Richards, W.D.; Dacek, S.; Cholia, S.; Gunter, D.; Skinner, D.; Ceder, G.; et al. Commentary: The Materials Project: A Materials Genome Approach to Accelerating Materials Innovation. APL Mater.
**2013**, 1, 011002. [Google Scholar] [CrossRef] - Sendek, A.D.; Cubuk, E.D.; Antoniuk, E.R.; Cheon, G.; Cui, Y.; Reed, E.J. Machine Learning-Assisted Discovery of Solid Li-Ion Conducting Materials. Chem. Mater.
**2019**, 31, 342–352. [Google Scholar] [CrossRef] - Cubuk, E.D.; Sendek, A.D.; Reed, E.J. Screening Billions of Candidates for Solid Lithium-Ion Conductors: A Transfer Learning Approach for Small Data. J Chem. Phys.
**2019**, 150, 214701. [Google Scholar] [CrossRef] - Ma, Y.; Guo, G. Support Vector Machines Applications; Springer: Berlin/Heidelberg, Germany, 2014; ISBN 9783319022994. [Google Scholar]
- Cristianini, N.; Shawe-Taylor, J. An Introduction to Support Vector Machines and Other Kernel-Based Learning Methods; Cambridge University Press: Cambridge, UK, 2000; ISBN 9780521780193. [Google Scholar]
- Miyamoto, S. Theory of Agglomerative Hierarchical Clustering; Behaviormetrics: Quantitative Approaches to Human Behavior; Springer Singapore: Singapore, 2022; Volume 15, ISBN 978-981-19-0419-6. [Google Scholar]
- Erbacher, M. Cluster Analysis; Atkinson, P., Delamont, S., Cernat, A., Sakshaug, J.W., Williams, R.A., Eds.; SAGE Publications Ltd.: New York, NY, USA, 2020; ISBN 9781529748222. [Google Scholar]
- Liu, J.; Han, J. Spectral Clustering. In Data Clustering; Chapman and Hall/CRC: Boca Raton, FL, USA, 2018; pp. 177–200. ISBN 9781315373515. [Google Scholar]
- Hosmer, D.W.; Lemeshow, S.; Sturdivant, R.X. Applied Logistic Regression, 3rd ed.; Wiley: New York, NY, USA, 2013; ISBN 9781118548387. [Google Scholar]
- Richards, W.D.; Miara, L.J.; Wang, Y.; Kim, J.C.; Ceder, G. Interface Stability in Solid-State Batteries. Chem. Mater.
**2016**, 28, 266–273. [Google Scholar] [CrossRef] - Luntz, A.C.; Voss, J.; Reuter, K. Interfacial Challenges in Solid-State Li Ion Batteries. J. Phys. Chem. Lett.
**2015**, 6, 4599–4604. [Google Scholar] [CrossRef] - Huo, S.; Sheng, L.; Xue, W.; Wang, L.; Xu, H.; Zhang, H.; Su, B.; Lyu, M.; He, X. Challenges of Stable Ion Pathways in Cathode Electrode for All-Solid-State Lithium Batteries: A Review. Adv. Energy Mater.
**2023**, 2204343. [Google Scholar] [CrossRef] - Eckhoff, M.; Schönewald, F.; Risch, M.; Volkert, C.A.; Blöchl, P.E.; Behler, J. Closing the Gap between Theory and Experiment for Lithium Manganese Oxide Spinels Using a High-Dimensional Neural Network Potential. Phys. Rev. B
**2020**, 102, 174102. [Google Scholar] [CrossRef] - Gao, B.; Jalem, R.; Ma, Y.; Tateyama, Y. Li+ Transport Mechanism at the Heterogeneous Cathode/Solid Electrolyte Interface in an All-Solid-State Battery via the First-Principles Structure Prediction Scheme. Chem. Mater.
**2020**, 32, 85–96. [Google Scholar] [CrossRef] - Kim, S.; Chen, J.; Cheng, T.; Gindulyte, A.; He, J.; He, S.; Li, Q.; Shoemaker, B.A.; Thiessen, P.A.; Yu, B.; et al. PubChem in 2021: New Data Content and Improved Web Interfaces. Nucleic Acids Res.
**2021**, 49, D1388–D1395. [Google Scholar] [CrossRef] [PubMed] - Materials Data Repository Home. Available online: https://materialsdata.nist.gov/ (accessed on 7 March 2023).
- Kirklin, S.; Saal, J.E.; Meredig, B.; Thompson, A.; Doak, J.W.; Aykol, M.; Rühl, S.; Wolverton, C. The Open Quantum Materials Database (OQMD): Assessing the Accuracy of DFT Formation Energies. Npj Comput. Mater.
**2015**, 1, 15010. [Google Scholar] [CrossRef] - Saal, J.E.; Kirklin, S.; Aykol, M.; Meredig, B.; Wolverton, C. Materials Design and Discovery with High-Throughput Density Functional Theory: The Open Quantum Materials Database (OQMD). JOM
**2013**, 65, 1501–1509. [Google Scholar] [CrossRef]

Approaches | Advantages | Disadvantages |
---|---|---|

Support vector regression (SVR) [89,90] | Effective models for small quantities of data, multiple Kernel functions available based on applications, and relatively high predictive power in supervised learning models. | Require careful research for function selections to avoid overfitting. |

Agglomerative hierarchical clustering [91,92] | No prior knowledge of the number of clusters is required; the approach does not require very large sample sizes to perform well. | Relatively large computational costs are required. |

Spectral clustering [93] | Perform well on small numbers of clusters and medium sample sizes. | Require prior knowledge of the number of clusters. |

Logistic regression [94] | The approach can be employed relatively easily in classification. | Non-linear problems are not applicable, but linear boundary data is relatively rare. |

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**MDPI and ACS Style**

Hu, S.; Huang, C.
Machine-Learning Approaches for the Discovery of Electrolyte Materials for Solid-State Lithium Batteries. *Batteries* **2023**, *9*, 228.
https://doi.org/10.3390/batteries9040228

**AMA Style**

Hu S, Huang C.
Machine-Learning Approaches for the Discovery of Electrolyte Materials for Solid-State Lithium Batteries. *Batteries*. 2023; 9(4):228.
https://doi.org/10.3390/batteries9040228

**Chicago/Turabian Style**

Hu, Shengyi, and Chun Huang.
2023. "Machine-Learning Approaches for the Discovery of Electrolyte Materials for Solid-State Lithium Batteries" *Batteries* 9, no. 4: 228.
https://doi.org/10.3390/batteries9040228